Lecture # 16: Review for Final Exam - Iowa State Universityhuhui/teaching/2011Sx/class-notes/AerE344... · AerE 344 Lecture Notes. ... easy to broke • Much more ... index of refraction

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Copyright © by Dr. Hui Hu @ Iowa State University. All Rights Reserved!

Hui HuDepartment of Aerospace Engineering, Iowa State University

Ames, Iowa 50011, U.S.A

Lecture # 16: Review for Final Exam

AerE 344 Lecture Notes


AerE343L: Dimensional Analysis and Similitude

Commonly used non-dimensional parameters:

force tension surfaceforce inertial WeNumber,Weber

force inertialforce lcentrifugaStr Number, Strohal

forcelity compressibforce inertialM Number,Mach

forcegravity force inertial

lgFr Number, Froude

force viscousforce inertialRe number, Reynolds

force inertialforce pressureEu number,Euler

2

2

lVVl

cV

V

VLVp

Similitude:• Geometric similarity: the model

have the same shape as the prototype.

• Kinematic similarity: condition where the velocity ratio is a constant between all corresponding points in the flow field.

• Dynamic similarity: Forces which act on corresponding masses in the model flow and prototype flow are in the same ratio through out the entire flow


Measurement Uncertainties

• “Error” is the difference between the experimentally-determined value and its true value; therefore, as error decreases, accuracy is said to increase.

• Total error, U, can be considered to be composed of two components:– a random (precision) component, – a systematic (bias) component,– We usually don’t know these exactly, so we estimate them with P and B, respectively.

222 PBU

XTrue valueX=100

Bias error

precision error

measured valueX=101

Repeatability Precision Error

Reproducibility Both Bias and Precision Errors

truemtruemeasurederror AAEAAA true

errorrelative A

AE


Measurement Uncertainties

pppV

BernoulliVpp

statictotal

statictotal

2)(2

)(,21 2

222RRR PBU

Uncertainty in velocity V:

J

ii

iR

J

ii

iR P

XRPB

XRB

1

22

1

22 ;

M

jii j

BB1

2

For a large number of samples (N>10) ii SP 2

N

kkii

N

kikii X

NXXX

NS

1

21

1

2 1;1

1


Pressure Measurement Techniques

• Deadweight gauges:• Elastic-element gauges:• Electrical Pressure transducers:• Wall Pressure measurements

– Remote connection– Cavity mounting– Flush mounting

• Pressure Measurements inside Flow Field:


)(2

)(,21

0

20

stat

stat

ppV

BernoulliVpp

• Advantage:

• Simple• cheap

• Disadvantage:• averaged velocity only• Single point measurements• Low measurement accuracy

Velocity measurement techniques – Pitot –Static Probe


Velocity measurement techniques – Hotwire Probe

• Advantage:• High accuracy• High dynamic response

• Disadvantage:• Single point measurements• Fragile, easy to broke• Much more expansive

compared with pitot-static probe.

Flow Field

Current flow through wire

The rate of which heat is removed from the sensor is directly related to the velocity of the fluid flowing over the sensor

V

• Constant-current anemometry• Constant-temperature anemometry

),(2ww

w TVqRidt

dTmc


AerE311L: The nature of light

• Light as electromagnetic waves.• Light as photons.• Color of light• Index of reflection

1/ 0 vcn

sm /3x10c 80


Shadowgraph and Schlieren technique

• Index of refraction:

• Depend on variation of index of refraction in a transparent medium and the resulting effect on a light beam passing through the test section

• Shadowgraph systems: are used to indicate the variation of the second derivatives (normal to the light beam) of the index of refraction.

• Schlieren Systems: are used to indicate the variation of the first derivative of the index of refraction

1/ 0 vcn

shadowgraph depicting the flow generated by a bullet at supersonic speeds. (by Andrew Davidhazy )

Schlieren images of the muzzle blast and supersonic bullet from firing a .30-06 caliber high-powered rifle (by Gary S. Settles )


Visualization of a Schockwaves using Schlieren technique

Before turning on the Supersonic jet

After turning on the Supersonic jet


Schlieren vs. Shadowgraph

Shadowgraph

• Displays a mere shadow• Shows light ray displacement• Contrast level responds to

• No knife edge used

Schlieren

• Displays a focused image• Shows ray refraction angle, • Contrast level responds to

• Knife edge used for cutoffyn

2

2

yn


Particle Image Velocimetry (PIV)

• To seed fluid flows with small tracer particles (~µm), and assume the tracer particles moving with the same velocity as the low fluid flows.

• To measure the displacements (L) of the tracer particles between known time interval (t). The local velocity of fluid flow is calculated by U= L/t .

A. t=t0 B. t=t0+10 sClassic 2-D PIV measurement

C. Derived Velocity fieldX (mm)

Y(m

m)

-50 0 50 100 150

-60

-40

-20

0

20

40

60

80

100

-0.9 -0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.95.0 m/sspanwise

vorticity (1/s)

shadow region

GA(W)-1 airfoil

t=t0 tLU

t= t0+tL

• Advantage:• Whole flow field measurements• Non-intrusive measurements

• Disadvantage:• Low temporal resolution• Very expansive compared with

hotwire anemometers and pitot-static probes.


PIV System Setup

Illumination system(Laser and optics)

cameraSynchronizer

seed flow withtracer particles

Host computer

Particle tracers: to track the fluid movement. Illumination system: to illuminate the flow field in the interest region.Camera: to capture the images of the particle tracers.Synchronizer: the control the timing of the laser illumination and

camera acquisition.Host computer: to store the particle images and conduct image processing.


Advanced PIV techniques

Measurement region80mm by 80mm

Laser sheet with P-polarization direction

Lobed nozzle

650mm

650mm

25 0

25 0

Synchronizer

cylinder lens Host computer

high-resolution CCD camera 3

Double-pulsed

Nd:YAG Laser set A

Polarizer cube

Polarizing beam splitter cubes

Mirror #3

Mirror #4

Half wave (/2) plateMirror #1

Mirror #2


Laser sheet withS-polarization direction

S-polarized laser beamP-polarized laser beam



Double-pulsed

Nd:YAG Laser set B

• Stereoscopic PIV technique

• Dual-plane stereoscopic PIV technique

• 3-D PTV technique

• Holograph PIV techniques

• Defocus PIV technique

Camera 1 Camera 2

Laser Sheet

1

2

Z

X

Stereo PIV technique


Laminar Flows and Turbulent Flows

'';' wwwvvvuuu

...),,,(1 0

0

Tt

t

dttzyxuT

u

0'0';0' wvu

0)'(0)'(;0)'(1)'( 2222

0

wvdtuT

uTt

t

o


Boundary Layer Flow

y

Uu 99.0,yat

Displacement thickness:

Momentum thickness:


Review of Quasi-1D Nozzle Flow

uduM

AdA )1( 2

M<1 M>1

Throat M=1

u increasing

M>1 M<1

Throat M=1

u decreasing


1st, 2nd and 3rd critic conditions

1st critic condition



P 0 in

crea

sing

P 0 in

crea

sing


Streamlines (experiment)

Lab #1: Flow visualization by using smoke wind tunnel

• Path line• Streak lines• Streamline


2

21*

*

VC

qCppp

T

EA

Test section

Contraction section

A

E

V

Settling chamber

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Linear curve fittingExperimental data

P = PA-PE (Pa)

q =0

.5*

V2

Lab#02: Wind Tunnel Calibration


Lab #3: Pressure Sensor Calibration and Uncertainty Analysis

• Task #1: Pressure Sensor Calibration experiment– A pressure sensor – Setra pressure transducer with a range of +/- 5 inH2O

• It has two pressure ports: one for total pressure and one for static (or reference) pressure.– A computer data acquisition system to measure the output voltage from the manometer.– A manometer of known accuracy

• Mensor Digital Pressure Gage, Model 2101, Range of +/- 10 inH2O

– A plenum and a hand pump to pressurize it. – Tubing to connect pressure sensors and plenum

• Lab output:– Calibration curve – Repeatability of your results– Uncertainty of your measurements

Setra pressure transducer

(to be calibrated)

Mensor Digital Pressure Gage A computer A plenum hand pump

tubing


Lab#04 Measurements of Pressure Distributions around a Circular Cylinder

22

2

2

2

2

sin41)sin2(1

1

21

VV

VV

V

PPCp

R

P

Incoming flow

X

Y

-3

-2

-1

0

1

0 100 200 300 400

Angle, Deg.

Cp

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6 7

theta (rad ) -->

cp --

>

EFDCFDAFD


Lab#05: Airfoil Pressure Distribution Measurements

NACA0012 airfoil with 32 pressure tabs

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14 16 18 20

CL=2Experimental data

Angle of Attack (degrees)

Lift

Coe

ffici

ent,

Cl

cV

LCl2

21

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20

Experimental data


Dra

g C

oeffi

cien

t, C

d

cV

DCd2

21

-3 .0-2 .5-2 .0-1 .5-1 .0-0 .5

00.51.01.52.02.53.0

0 1 2 3 4 5 6 7 8 9 10 11 12

X (inches)

Y (in

ches

)

1

5 1222

253040

47


y

x80 mm

Pressure rake with 41 total pressure probes(the distance between the probes d=2mm)

Lab 06: Airfoil Wake Measurements and Hotwire Anemometer Calibration

y

x

2

2

22

2

2

)])(1()([221

)])(1()([

21

dyU

yUU

yUC

C

CU

dAU

yUU

yUU

CU

DC

D

D


Lab 07: Hot wire measurements in the wake of an airfoily

x

80 mm

Pressure rake with 41 total pressure probes(the distance between the probes d=2mm)

Hotwire probe

Test conditions: Velocity: V=15 m/sAngle of attack: AOA=0, and 12 deg.Date sampling rate: f=1000HzNumber of samples: 10,000 (10s in time)No. of points: 20~25 pointsGap between points: ~0.2 inches

Lab#3

Lab#4


Lab#08: Measurements of Boundary Layer over a Flat Plate

XY

Pitot rake

Displacement thickness:

Momentum thickness:

• To conduct velocity profile measurements at 10 downstream locations.

• To determine boundary layer thickness and drag coefficient based on the velocity measurement results.

LCd

2Drag coefficient:


AerE343L Lab#6: PIV Measurements of a Flapping Wing

X (mm)

Y(m

m)

0 20 40 60

-20

-10

0

10

20

30-1.00 -0.60 -0.20 0.20 0.60 1.00

Spanwise Vorticity(1000*1/s)

X (mm)

Y(m

m)

0 20 40 60

-20

-10

0

10

20

30 -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20

Spanwise Vorticity(1000*1/s)

Flapping frequency: f = 60HzChord length: C = 12.7mmWing span: L = 76.7 mmFlow velocity: V = 6.36 m/s

Flapping frequency: f = 60HzChord length: C = 12.7mmWing span: L = 76.7 mmFlow velocity: V = 1.44 m/s


Lab#09: Visualization of Shockwaves using Schlieren technique

Under-expanded

flow

Flow close to

3rd critical

Over-expanded

flow

2nd critical –shock is at nozzle exit

1st critical –shock is

almost at the nozzle throat.

Tank with compressed air Test section


Lab#10: Set Up a Schlieren and/or Shadowgraph System to Visualize a Thermal Plume

Point Source

Candle plume


Tank with compressed air Test section

Lab#11: Pressure Measurements in a de Laval Nozzle

Tap No. Distance downstream of throat (inches) Area (Sq. inches)1 -4.00 0.8002 -1.50 0.5293 -0.30 0.4804 -0.18 0.4785 0.00 0.4766 0.15 0.4977 0.30 0.5188 0.45 0.5399 0.60 0.56010 0.75 0.58111 0.90 0.59912 1.05 0.61613 1.20 0.62714 1.35 0.63215 1.45 0.634


X/C *100

Y/C

*100

-20 0 20 40 60 80 100 120

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12 14 16 18 20

CL=2Experimental data


Lift

Coe

ffici

ent,

Cl

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 2 4 6 8 10 12 14 16 18 20

Experimental data


Dra

g C

oeffi

cien

t, C

d

X/C *100

Y/C

*100

-40 -20 0 20 40 60 80 100 120 140

-60

-40

-20

0

20

40

60

vort: -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5

shadow region

GA(W)-1 airfoil

25 m/s

Airfoil stall

Airfoil stall

Before stall

After stallcV

DCd2

21

cV

LCl2

21

Lab#12: PIV measurements of the Unsteady Vortex Structures in the Wake of an Airfoil


Lab#13: Stereoscopic PIV technique and Applications

Camera 1 Camera 2

Laser Sheet

1

2

Z

X

Displacement vectors in left camera Displacement vectors in right camera

Stereo PIV technique

.deg0.5;000,52Re C

X/C =4.0

X pixel

Ypi

xel

0 500 1000 1500

0

200

400

600

800

1000

1200

X pixel

Ypi

xel

0 500 1000 1500

0

200

400

600

800

1000

1200


AerE344: Final Exam

• Since many of the students were scheduled to take three final exams

(AerE321L, AerE331 and AerE344) on Monday May 2, according to

ISU's policy, the final exam of AerE344/AerE490A/AerE490B has been

rescheduled to Tuesday, May 3 from 2:15pm -4:15pm at GILMAN 1352.

• Open book and open class notes.

• 20 multiple-choice problems (2 points each).

• Four regular problems related to Lab design and lab report (15 points

each).

• Exam time: 120 minutes.

Documents

Lecture # 16: Review for Final Exam - Iowa State Universityhuhui/teaching/2011Sx/class-notes/AerE344... · AerE 344 Lecture Notes. ... easy to broke • Much more ... index of refraction